Rmt 2marks - Lecture notes 1,2,3,4,5 PDF

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REJINPAUL QUESTION BANK CS6704 -RESOURCE MANAGEMENT TECHNIQUES QUESTION BANK VII SEMESTER

SYLLABUS UNIT I LINEAR PROGRAMMING

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Principal components of decision problem – Modeling phases – LP Formulation and graphic solution –Resource allocation problems – Simplex method – Sensitivity analysis. UNIT II DUALITY AND NETWORKS 9 Definition of dual problem – Primal – Dual relation ships – Dual simplex methods – Post optimality analysis – Transportation and assignment model - Shortest route problem. UNIT III INTEGER PROGRAMMING 9 Cutting plan algorithm – Branch and bound methods, Multistage (Dynamic) programming. UNIT IV CLASSICAL OPTIMISATION THEORY: 9 Unconstrained external problems, Newton – Ralphson method – Equality constraints – Jacobean methods – Lagrangian method – Kuhn – Tucker conditions – Simple problems. UNIT V OBJECT SCHEDULING: 9 Network diagram representation – Critical path method – Time charts and resource leveling – PERT. TEXT BOOK: 1. H.A. Taha, “Operation Research”, Prentice Hall of India, 2002. REFERENCES: 1. Paneer Selvam, ‘Operations Research’, Prentice Hall of India, 2002 2. Anderson ‘Quantitative Methods for Business’, 8th Edition, Thomson Learning, 2002. 3. Winston ‘Operation Research’, Thomson Learning, 2003. 4. Vohra, ‘Quantitative Techniques in Management’, Tata Mc Graw Hill, 2002. 5. Anand Sarma, ‘Operation Research’, Himalaya Publishing House, 2003. UNIT I -LINEAR PROGRAMMING

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Principal components of decision problem – Modeling phases – LP Formulation and graphic solution –Resource allocation problems – Simplex method – Sensitivity analysis. 1. What is linear programming? Linear programming is a technique used for determining optimum utilization of limited resources to meet out the given objectives. The objective is to maximize the profit or minimize the resources (men, machine, materials and money) 2. Write the general mathematical formulation of LPP. 1. Objective function

Max or Min Z = C1x1 + C2x2+ …..+ Cnxn 2. Subject to the constraints a11x1+a12x2+…………+ a1nxn (≤=≥)b1 a21x1+a22x2+…………+ a2nxn (≤=≥)b2 ………………………………………………………….. …………………………………………………………..

am1x1+am2x2+…………+ amnxn (≤=≥)bm 3. Non-negative constraints x1,x2,….xm≥ 0 3. What are the characteristic of LPP?  There must be a well defined objective function.  There must be alternative course of action to choose.  Both the objective functions and the constraints must be linear equation or inequalities. 4. What are the characteristic of standard form of LPP?  The objective function is of maximization type.  All the constraint equation must be of equal type by adding slack or surplus variables  RHS of the constraint equation must be positive type  All the decision variables are of positive type 5. What are the characteristics of canonical form of LPP? (NOV ’07) In canonical form, if the objective function is of maximization type, then all constraints are of ≤ type. Similarly if the objective function is of minimization type, then all constraints are of ≥ type. But non-negative constraints are ≥type for both cases. 6. A firm manufactures two types of products A and B and sells them at profit of Rs 2 on type A and Rs 3 on type B. Each product is processed on two machines M1 and M2.Type A requires 1 minute of processing time on M1 and 2 minutes on M2 Type B requires 1 minute of processing time on M1 and 1 minute on M2. Machine M1 is available for not more than 6 hours 40 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as a LPP so as to maximize the profit. (MAY ’07) Maximize z =2x1 +3x2 Subject tot the constraints: x1 + x2 ≤ 400 2x1 + x2 ≤ 600 x1 ,x2≥ 0 7. A company sells two different products A and B , making a profit of Rs.40 and Rs. 30 per unit on them,respectively.They are produced in a common production process and are sold in two different markets, the production process has a total capacity of 30,000 man-hours. It takes three hours to produce a unit of A and one hour to produce a unit of B. The market has been surveyed and company official feel that the maximum number of units of A that can be sold is 8,000 units and that of B is 12,000 units. Subject to these limitations, products can be sold in any combination. Formulate the problem as a LPP so as to maximize the profit Maximize z =40x1 +30x2 Subject tot the constraints: 3x1 + x2 ≤ 30,000 x1 ≤ 8000 x2 ≤ 12000

x1 ,x2≥ 0 8. What is feasibility region? (MAY ’08) Collections of all feasible solutions are called a feasible set or region of an optimization model. Or A region in which all the constraints are satisfied is called feasible region. 9. What is feasibility region in an LP problem? Is ti necessary that it should always be a convex set? A region in which all the constraints are satisfied is called feasible region. The feasible region of an LPP is always convex set. 10. Define solution A set of variables x1,x2….xn which satisfies the constraints of LPP is called a solution. 11. Define feasible solution? (MAY ’07) Any solution to a LPP which satisfies the non negativity restrictions of LPP’s called the feasible solution 12. Define optimal solution of LPP. (MAY ’09) Any feasible solution which optimizes the objective function of the LPP’s called the optimal solution

13. State the applications of linear programming  Work scheduling  Production planning & production process  Capital budgeting  Financial planning  Blending  Farm planning  Distribution  Multi-period decision problem Inventory model Financial model Work scheduling 14. State the Limitations of LP.  LP treats all functional relations as linear  LP does not take into account the effect of time and uncertainty  No guarantee for integer solution. Rounding off may not feasible or optimal solution.  Deals with single objective, while in real life the situation may be difficult. 15. What do you understand by redundant constraints? In a given LPP any constraint does not affect the feasible region or solution space then the constraint is said to be a redundant constraint. 16. Define Unbounded solution? If the feasible solution region does not have a bounded area the maximum value of Z occurs at infinity. Hence the LPP is said to have unbounded solution. 17. Define Multiple Optimal solution? A LPP having more than one optimal solution is said to have alternative or multiple optimal solutions. 18. What is slack variable?

If the constraint as general LPP be = type then a non negative is introduced to convert the inequalities into equalities are called the surplus variables. 20. Define Basic solution? Given a system of m linear equations with n variables(m...